On the total number of parts functions associated with ranks of partitions modulo 5 and 7
Tóm tắt
Recently, Andrews proved congruences for the total number of parts functions associated with ranks of partitions modulo 5 and 7. In this paper, applying the method of Atkin and Swinnerton-Dyer, we establish identities for these functions from which Andrews’ congruences modulo 5 follow immediately. In particular, the generating functions for total number parts functions associated with ranks of partitions modulo 7 turn out to be theta-functions.
Tài liệu tham khảo
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